Math to learn over summer?

<p>I'm interested in learning some math over summer and during senior year.</p>

<p>I'm a high school junior who took calc BC and did pretty well. However, I'll be taking stats next year because my school doesn't offer multivariable. I considered the option of taking MV at the local community college, but the transporation + etc isn't feasible.</p>

<p>Nevertheless, I'd like to learn some math over summer and during senior year. I believe the course after calc BC is usually multivariable. However, I'm mostly interested in developing a strong math foundation for college classes. I've heard that linear algebra differs from calc, which is a lot of repetition.</p>

<p>What should I learn over summer to give me a small idea of what college math will be like? I found that calc BC was mostly learning formulas and applying them. Should I learn MV calc, or try linear algebra? Thanks for any help</p>

<p>Why not learn different kinds of math?
Discrete math for example. Although it is technically not "after" any math class, it is still interesting and useful.</p>

<p>Linear algebra is so much fun. Different from anything that you've seen before, but definitely a rewarding subject to master.</p>

<p>I'm not sure what exactly to advise, for the following reason - topics like linear algebra really only made sense to me once I encountered them in college work for a while, over and over. Learning the subject by itself seems like you'll be manipulating symbols a lot. That's how I felt the first time I saw it [which was well before college, hence why I chose to comment]. </p>

<p>As a young math student, if you can, when you learn stuff like multivariable and linear algebra, perhaps see if you can look at where these things show up, for instance in a good physics textbook. Lots of E&M books [like Griffiths, Purcell] should be in the language of MV calculus. Linear algebra should show up in any good intro to quantum mechanics. I think it's important that once you get past calculus in the single variable, which has very streamlined applications, to keep in mind that all these theories have lots of meaning. </p>

<p>To really learn these things well and get something very substantial preparation for college math, you probably should take the approach I've told you, but if you don't, you'll still get something out of it, just not, in my opinion, close to the same pleasure and insight.</p>

<p>Something to think about though:</p>

<p>
[quote]
I found that calc BC was mostly learning formulas and applying them.

[/quote]
</p>

<p>Calculus goes beyond this. There's meaning to all that you did. Why not pick up a proper book like Apostol and learn calculus properly (i.e. what the stuff means, where the results you use came from) instead of learning to manipulate symbols involving vector spaces and matrices [in basic linear algebra}?</p>

<p>On second thought, this is all probably way too much to ask of you to do in a year.</p>

<p>I'd say if you want to do something good for yourself, learn calculus the proper way using Apostol, have a peek at the theorems in linear algebra, and be sure you try some physics using calculus in a serious way [which prob. means learning some multivariable calculus]. The quantum mechanics bit is probably better done in college properly.</p>

<p>I would recommend something fun like: An Introduction to Probability Theory and Its Applications, Vol. 1</p>

<p>I found Apostol to be dry and painful. Feller's book presents some really cool situations that I enjoyed reading about (eg, counting ballots and the chance that someone is ahead while you're in the process of counting). I'm not sure if this book is really accessible to a high school senior though (Apostol's is surely pushing what I could tolerate as a high schooler).</p>

<p>I would actually recommend problem solving books like Art of Problem Solving if you haven't tried those before. Those are meant for high-schoolers and have fun problems.</p>

<p>thanks for the advice :)</p>

<p>yeah, I've been thinking about using the Art of Problem solving books. they look interesting.</p>

<p>You should definitely get the Art of Problem Solving books - they are, simply put, fantastic. Also they just came out with a calculus book, which would be ideal to study from if you're wishing to gain a better understand of calculus.</p>

<p>AoPS = <3 </p>

<p>10char</p>